The volume of a cube is given by the formula:

\(V = x^3\)

To find the rate of change of the volume with respect to time, we use the chain rule:

\(\frac{dV}{dt} = \frac{dV}{dx} \times \frac{dx}{dt}\)

First, find \(\frac{dV}{dx}\):

\(\frac{dV}{dx} = 3x^2\)

We are given \(\frac{dx}{dt} = 0.01\) cm/min.

Substitute \(x = 20\) into the expression:

\(\frac{dV}{dt} = 3 \times 20^2 \times 0.01\)

Calculate:

\(\frac{dV}{dt} = 3 \times 400 \times 0.01 = 12\)

Therefore, the rate of increase of \(V\) when \(x = 20\) is 12 cm³/min.